Sampling, Ordering, Interleaving

Transcription

1 Sampling, Ordering, Interleaving Sampling patterns and PSFs View ordering Modulation due to transients Temporal modulations Slice interleaving Sequential, Odd/even, bit-reversed Arbitrary Other considerations: IR, MT, etc 328

2 Sampling & Point-Spread Functions PSF = Fourier transform of sampling pattern k-space: Extent, Density, Windowing PSF: Width, Replication, Ripple (side-lobes) k-space Sampling Point-Spread Function Fourier Transform Extent Spacing Width FOV 329

3 The Discrete sinc function h(x) = k sin( N kx) sin( kx) Function of extent Shows challenge of low N 330

4 Variable Density Sampling 2x undersamling Δk linear with k Minor Aliasing PSF broadens 331

5 Variable Density Sampling: Density Compensated Multiply by 1/Δk No PSF Broadening Higher ringing (center less dominant) need to apodize 332

6 Non-Cartesian Sampling / Gridding Irregularly sampled data Resample to grid to perform DFT k y k y k x k x 333

7 Divide samples by density at location k Want to have uniform signal if we grid 1 s Convolve sampled k locations with kernel c(k) Resample at grid points FFT Reconstruction De-apodize to undo convolution side effects Gridding Steps k y Jackson 1991 k x 334

8 Partial Fourier and PSF Full k-space trajectory is Sf(k), psf is δ(r) Half-k-space trajectory is Sh(k), PSF is sh(r) Sh(k) is real, with even component 0.5 Sf(k) Real{sh(r)} = 0.5 δ(r) Sampling: M(k) Sh(k) m(r)*[0.5 δ(r) + Imag{sh(r)}] If m(r) is real, the image is the real-part of m(r)*sh(r). How can we remove phase when m(r) is complex? 335

9 Partial k-space PSF - Contiguous Odd component is a step function Imaginary PSF is localized 336

10 Partial k-space PSF - Even/Odd Odd component is a step function modulated by e iπn Imaginary PSF is localized and shifted 337

11 Partial k-space PSF - Random Selection Odd component is random 0 or 1 Imaginary PSF is spread out 338

12 Homodyne Reconstruction Sample half k-space plus a little extra Symmetric k-space: low-resolution image phase φ(r) m(r) Use ramp filter to reconstruct m(r)*sh(r) Remove phase: [m(r)*sh(r)] e - φ(r) If sh(r) is narrow, phase of m(r) is canceled, and realpart leaves m(r)* δ(r) See John Pauly s notes for other recon methods 339

13 Partial Fourier Acquisition/Reconstruction k y F.T. k x k y Phase F.T. k x 340

14 Homodyne (k-space interpretation) From McGibney MRM 1993 H(u) ~ Density Compensation, reduced ringing Assumption Θ(u) is narrow 341

15 k-space Modulation Many sequences acquire multiple lines with transient magnetization Echo trains: T2 and T2* decay over k-space Magnetization-prepped bssfp, RF-spoiled transients Off-resonance (EPI, Spiral primarily) Temporal signal effects (non-motion): Contrast uptake, inflow, varying B0, 342

16 View Ordering / Grouping Sequential k y k x Centric / Center-out k y k x Interleaved k y Segmented k y k x k x 343 Each color is a different modulation (echo, time, etc)

17 3D Image (ky-kz) View Ordering/Grouping Sequential kz Sequential ky Center-out (φ,kr) k z k z k z k y k y k y Centric (ordered by radius first or azimuth (φ) first) Segment groups by ky, kz, φ, kr Sub-segment groups (ky, kz, φ, kr, randomly) 344

18 Modulation and PSFs Group k-space samples by intensity Reconstruct PSF for each group Multiply by modulation and sum 345

19 Modulation Example 1: FSE Echo Train of 2T2 Peak reduction (area) Decompose Modulation into even / odd parts real{psf} good PSF broadens 346

20 Modulation Example 2: PD FSE Echo Train of 2T2 Peak reduction (area) Symmetric modulation: Real PSF PSF broadens 347

21 Example: Echo-Train + CS + Half-Fourier + Elliptic smooth modulation with echo train Random sampling for CS Choose trajectories through regions to minimize change (eddy-current) Random ky-kz SEMAC sampling with partial ky and elliptic Worters 2011

22 Question: Temporal Odd/Even Sampling Sample odd-then-even lines during contrast uptake What will artifact look like if signal change is 2x frame rate? What can we do about it? Parallel image reconstruction (2x frame rate!) k y Aliased flicker True 2x Frames k x 349

23 Temporal Sampling (kf and k-t) Temporal SENSE R=3 Ordering k TE3 k f TE2 k x t TE1 350

24 Temporal Undersampling: DISCO Temporal Footprint Temporal Resolution 351

25 Temporal Undersampling: PSFs Data Acquisition (ky-kz -space) DISCO, TWIST Cartesian Acquisition with Projection Reconstruction (CAPR) Time-Resolved Imaging of Contrast Kinetics (TRICKS) Madhuranthakam 2006 Korosec 1996 Point-Spread Functions 352

26 Slice Interleaving Multislice acquisitions allow volumetric imaging Acquisitions can be sequential or interleaved Interleaving time efficient if there is dead time Different ways to interleave (reduce adjacent-slicesaturation) Sequential: 0, 1, 2, 3, 4, 5, 6, 7 Odd/Even: 0, 2, 4, 6, 1, 3, 5, 7 Bit-reversed: 0, 4, 2, 6, 1, 5, 3, 7 353

27 How Many Slices to Interleave? Usually specify TR, TI, Echo-train-length (ETL), Resolution,... Tells pulse durations (Tseq) and RF power Nmax ~ TR / Tseq Can re-order slices in time slots Additional slices require another acquisition Slice 0 Slice 1 Slice 2 Slice 0 RF TR 354

28 More Flexible Interleaving If Nslices > Nmax, scan is 2x, 3x,... longer Decoupling phase encode number allows flexible interleaving Read-out matrices across then down Slice Number Slice Number Outer Loop Outer Loop Inner Loop Pop/View Number Inner Loop Outer Loop Outer Loop Inner Loop Pop/View Number Inner Loop

29 FLAIR / STIR? Additional dead-time during TI interval Can sometimes interleave other acquisitions Additional constraints on TR, TI, Tseq Inversion Imaging RF TI TR 356

30 Summary Sampling and PSFs Resolution, FOV, ringing Variable-density and gridding Partial Fourier View ordering and k-space modulation ky-kz and k-t sampling Slice interleaving 357